The ideal boiling time for eggs in an induction cooker is typically around 6 to 8 minutes for a hard-boiled egg. This duration ensures that the egg whites are fully set and the yolks are firm but still slightly runny, which is often preferred for a perfect hard-boiled egg. The precise time can vary slightly depending on the size of the eggs and the power setting of the induction cooker.

The reason for this boiling time lies in the principle of heat transfer in induction cookers. Induction cookers work by generating a magnetic field that heats the pot directly, rather than heating the air around it like traditional electric or gas cooktops. This targeted heat transfer allows for a more precise control of the cooking temperature, which is crucial for boiling eggs. When the water reaches a rolling boil, the eggs should be added to the pot. Since the induction cooker maintains a consistent high heat, the eggs will cook more quickly than on a conventional stove.

Research conducted by the USDA (United States Department of Agriculture) suggests that a hard-boiled egg will reach the desired level of doneness within 6 to 8 minutes when boiled at a rolling boil. The USDA's guidelines for safe food handling recommend boiling eggs for at least 3 minutes after water reaches a rolling boil to ensure they are safe to eat. However, for the perfect texture, the additional 3 to 5 minutes of cooking time is necessary to achieve the desired firmness in the whites and the slightly runny yolks.

In conclusion, boiling eggs in an induction cooker for 6 to 8 minutes is the optimal cooking time to achieve a hard-boiled egg with a firm white and a slightly runny yolk. This duration is supported by the principles of heat transfer in induction cookers and the guidelines provided by the USDA for safe food handling.